Question

The APR of Lillian's savings account is 3.4%, and interest is compounded semiannually. If Lillian makes no additional deposits or withdrawals for an entire year, what will be the balance of her account after all the interest is paid for the year on a principal balance of $9700?

Answer 1

The correct answer is:
$10,032.60.

Step-by-step explanation:
The formula for compound interest is:
A=p(1+
`(r)/(n)`)^(nt),
where:
A is the total amount,
p is the amount of principal,
r is the interest rate as a decimal number,
n is the number of times per year the interest is compounded
t is the number of years.

We know that:
p=9700,
r=3.4%= 0.034,
n=2, and
t=1

A=9700(1+
`(0.034)/(2)`)²ˣ¹=9700(1+0.017)²=9700(1.017)²=10032.60.

Answer 2

The equation for that is

A = P * [ 1 + (r/n) ] ^(nt)

A = amount of money accumulated after n years, including interest.
P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
n = number of times the interest is compounded per year
t = number of years the amount is deposited or borrowed for.

In this question, P = 9700 , r = 0.034, n = 4 , t = 1

A = 9700 * [ 1 + (0.034 / 4) ] ^ (4 * 1)

= 9700 * ( 1 + 0.0085 )^4

= 9700 * (1.0085)^4

= 9700 * 1.03443596

= 10,032.60 rounded off